Abstract. The primeval solar nebula hypothesis, the mainstream
theory of solar system formation for over 200 years and a product of inductive
reasoning, is wrong. It cannot explain much of what we know about the solar
system today, and has failed to make useful substantive predictions. Rather,
each new discovery requires a new explanation for how it can fit into the
theory. By contrast, deductive reasoning leads us to fission theory as the
logical origin of today’s major planets and non-asteroidal moons, with the
exploded planet hypothesis accounting for small solar system bodies. In the
decade since this model was formulated deductively, it has made several
significant and successful predictions, led to explanations lacking in
paradoxes, pointed to previously unrecognized patterns, and given us insights
about planets and moons that no longer exist.

The primeval solar nebula hypothesis (PSNH) is the
mainstream theory of solar system formation in the field of astronomy today. It
is a modern variant of a theory put forward by Pierre Laplace in 1796 – so
variant that Laplace would hardly recognize it. In PSNH, the Sun, its major
planets and their natural moons all formed from the cooling and condensing of a
rotating cloud of interstellar gas and dust. As a large blob formed somewhere
inside this cloud, matter began to fall toward it, causing the cloud to spin up
and flatten. The large blob continued to grow and eventually became the Sun.
Then the largest of the other revolving lumps in this nebula condensed into
major planets. These in turn attracted more gas and dust to fall toward the
planets, and began to revolve around them. The largest clumps therein grew into
the natural moons of the planets. Jupiter’s gravity prevented formation of a
planet in the main asteroid belt, where asteroids are found. And the formation
of Uranus and Neptune pumped up the orbits of many smaller icy bodies, leading
to the Trans-Neptunian Objects (TNOs) and the Oort cloud of comets 1000 times
farther away from the Sun.

The problems with this theory are many, requiring continual
help from ad hoc helper hypotheses.
First, interstellar gas and dust clouds don’t have significant rotation, so it
is difficult to get such a cloud to flatten. It is now usually recognized that
something like the blast wave from a supernova explosion is needed to flatten
the cloud. Today, the Sun contains over 99% of the solar system’s mass, yet surprisingly
only 1% of its angular (rotational) momentum. The PSNH theory proposes magnetic
forces between Sun and planets to explain this puzzle, but details consistent
with today’s solar system have been lacking. Even more serious, attempts to
explain the dominance of prograde orbital motion and rotation for planets and
moons have been entirely unsuccessful.

Mathematical modeling of PSNH homed in on computer models
that produced solar-system-like outcomes. But newly discovered exoplanetary
systems around other stars have found many Jupiter-sized planets near their
parent stars, which these models forbid; and many high-eccentricity orbits,
which are supposed to be rare. Jupiter’s gravity creates a zone of enhanced
stability in the main asteroid belt, the exact opposite of being a force
disrupting planetesimal formation. Moreover, small bodies with mutually similar
solar orbits cannot accrete because gravitational forces make them librate and
avoid collisions; whereas small bodies with dissimilar orbits tend to collide
destructively because of high relative speeds. The sharpness of the observed “Oort
cloud” property of comets orbits has proved difficult to reconcile with the
model’s expectation of a much broader distribution of mean distances from the
Sun. The presence of argon and nitrogen found by the Galileo spacecraft in Jupiter’s atmosphere is inconsistent with the
expected temperatures at Jupiter’s formation distance from the Sun. James
Maxwell showed that the shear forces from a disk with differential rotation
would have prevented the condensation of individual planets. Sir James Jeans
studied the breakup of spinning bodies from centrifugal forces and also concluded
that formation of the solar system from a single co-rotating gaseous cloud was
not dynamically possible. (Britannica Online 2008)

It seems safe to say that, but for all the history,
textbooks, papers, funding, careers, and reputations at stake, the field would
readily embrace a viable alternative model free of all these problems.
Amazingly, such a model now exists.

Competing theories

Ironically, the original Laplace “nebular hypothesis”,
before it had to be manipulated in so many ways, contains the kernel of a model
that actually works. Laplace had the proto-Sun’s atmosphere extending beyond
the distance at which any planets form. Next, he assumed the Sun would cool and
contract as it radiated away its heat. Contraction would force speed-up of the
various atmospheric layers. At each layer where gravity and centrifugal force
balance, collisions would deposit a ring of material in the Sun’s equatorial
plane. Each such ring would then coalesce into a planet. Moons would form by a
similar process around planets.

We now know that rings do not coalesce, but will instead
disperse to the maximum extent possible so that collisions are minimized or
avoided altogether. But modern ideas agree that the early proto-Sun was a very
extensive body and might easily have extended well beyond Neptune’s orbit.
Laplace simply did not have knowledge of how such a body would behave as it
continued to accrete more infalling gas and dust. If he had, he would have been
led directly to the fission model.

The fission model as it exists today was elucidated in Van
Flandern (1997b) and Van Flandern (1999) with a minor update in Van Flandern
(2004). The following section will give the most detailed description of the
specifics of the model yet developed by any author.

The fission model for planet formation

Summary: A supernova sends out a blast wave, which flattens an
interstellar cloud. Gravitational collapse of the flattened cloud forms one or
more proto-stars, which contract and spin-up as they accrete gas and dust. Spin
makes the proto-star’s shape oblate, and faster spin makes it prolate, This
leads to overspin and finally fission, forming planets.

1. A nebula gets flattened by a shock wave.

We start with a nebula, a three-dimensional cloud of gas and
dust, of the type seen frequently throughout our Galaxy, often created by
matter from previous generations of exploded stars. Such nebulas are normally
too large and dispersed for collapse from self-gravitation before other factors
change the nebula. One such factor is likely to be the shock wave from a nearby
supernova explosion. This must eventually happen, and tends to compress the
nebula in the direction of travel of the blast wave, creating a pancake shape.
(See Appendix A for more details on why it flattens the nebula.) This greatly
increases the density of the gas and dust everywhere in the nebula, making
gravitational collapse easier and faster. Gravity will ensure that the randomly
densest regions will collapse first. The original gas cloud is flattened rather
than scattered because all its molecules of whatever mass are quickly given
roughly the same speed as the supernova blast wave at just the time when the
blast wave passes. As a result, most of the cloud’s molecules end up with a
similar distance from the supernova and velocity through space when the blast
wave dissipates. The densest concentrations of molecules are then the sites for
potential star formation in a new generation cluster.

2. Gravity and collisions make dense regions denser and
hotter, eventually forming a proto-star.

Because the individual gas and dust molecules have small,
random motions of their own, they do not simply fall straight toward the
nearest high-density anomaly. But their motion is modified somewhat toward that
direction, which causes them to further increase the density of an already
over-dense region as they pursue a low orbit around it. Of course, the lower
such particles dip into the over-dense region, the greater is the probability
of a collision with another particle. Head-on collisions lowering one or both
particle velocities relative to other velocities in the over-dense region, and heating
both particles, would be common. (See Appendix B for the meaning of “heat” for
small particles.) These collisions tend on average to drop particles into still
lower orbits with even greater collision probabilities. The end result of
cascading collisions is to form a proto-star, with highest particle density and
heat in the center, gradually tapering off in density and heat with distance
until it blends smoothly into the average density of the surrounding pancake
nebula.

3. As central density further increases, the proto-star
becomes a liquid.

Note that collisions far from the center of a forming
proto-star are still mostly disruptive because of high relative speeds.
Particles in such collisions tend to bounce rather than stick; and tend to
break apart particles that may have already stuck together. Only near the
center can densities get so high that particles are forced into continuous
contact and a contiguous mass begins to form. If a secondary density
concentration started to form elsewhere, continuous high-speed bombardment from
particles orbiting the primary would most likely dissipate it before its
density could approach that of a contiguous mass. But in the center, the cloud
of gas and dust with free molecules becomes a liquid by virtue of having
contiguous molecules in contact, able to vibrate but not to move independent of
their neighbors. Meanwhile, farther from the center, planetary formation and
even moon formation have little chance of occurring in the manner envisioned in
the PSNH because collisions are mostly destructive and tend to heat things up.
(See Appendix C for more on the distinction between solid, liquid, and gaseous
phases.)

4. The proto-star and its atmosphere contract and start to
spin as accretion continues.

Continuing our deductive reasoning to see where it leads,
gravity would continue to attract particles from the larger nebula, and random
collisions would tend to bring down particles already in a vast extended
atmosphere around the forming proto-star. Particles falling from greater
distances would increase their radial and transverse speeds, but acquire
relatively little motion normal to the pancake-shaped nebula. Purely by chance,
the net number of collisions resulting in clockwise (CW) motion of the
colliding particles may outnumber the net number producing counterclockwise
(CCW) motion; or vice versa. Because we can view the pancake from either side,
we are free to choose the side consistent with the astronomers’ convention that
the resulting dominant motion will be CCW as seen from above, which is then
“north” by definition. The forming proto-star and its extended atmosphere
develop a unique spin.

5. The net motion in the proto-star atmosphere sets up
rotation with speed increasing inward.

As soon as the proto-star’s atmosphere acquires a dominant
rotation direction, however slight, collisions between particles going the
“wrong way” (CW) will be more frequent than collisions between “right way”
(CCW) particles. So CW particles tend to get corrected into CCW particles. At
the same time, average speeds are being lowered by collisions, causing further
contraction and heating of the atmosphere and liquid proto-Sun. But as particle
orbits lower, their average speeds must increase to conserve angular momentum.
The farther inward the gravity-controlled particle drops, the faster will be
the CCW motion it encounters. So the proto-star and its atmosphere take on a
preferred rotation direction, and the particles gradually sort themselves out
by eliminating velocity-cancelling CW particles and particles with radial
motions. This will get all particles moving at appropriate speeds for stable,
near-circular orbits at their own distance from the proto-star center. This is
the case except at small distances where the density has become high enough to
cause friction to dominate gravity in controlling particle motions. Near the
center, the forming contiguous liquid grows in size.

6. Continued contraction increases spin, then gravity and
cohesion compete to find a new equilibrium.

Layers in the proto-star and its atmosphere at different
distances rotate at different rates, as is necessary to balance gravitational
and centrifugal forces and keep the shape stable. But the continuing accretion
induces further contraction, which forces further spin-up to conserve angular
momentum. This process creates a stability problem. Angular momentum is
proportional to the product of distance and orbital velocity. To conserve it, a
distance decrease must be accompanied by a corresponding velocity increase, which
will then be inversely proportional to distance; i.e., at ¼ the distance the
velocity will be 4 times as great. However, to maintain an equilibrium between
the central gravitational force and the centrifugal force at that distance, as
required for orbits to remain circular, the velocity must be inversely
proportional to the square root of distance; i.e., at ¼ the distance the
circular velocity will be twice as great. These two conditions are
incompatible. A contraction that conserves angular momentum will force the
rotation rate to be too high for that distance. This cohesion vs. gravity
competition, or “cograv effect” for short, resolves in one of the following
ways:

·For the central parts of the proto-star, the molecules are
already in contact, so cohesive forces override gravitational forces and the
liquid body simply spins faster and the shape deforms to the extent that
cohesion allows.

·For the sparse outer parts of the proto-star atmosphere,
gravity still dominates, so all the molecules at each distance are forced to
rise to the distance where gravity and centrifugal force again balance. In
brief, while the proto-star is contracting and driving mass inward toward its
center, the angular momentum of the arriving molecules is being driven outward
and away from the center where there is relatively little mass. (Here we see
the beginning of the resolution of the famous angular momentum paradox – why
the Sun with most of the mass has only ~1% of the solar system’s angular
momentum.)

·For intermediate parts of the proto-star atmosphere, both
processes operate. Centrifugal force tries to drive the molecules and their
angular momentum outward, slowing orbital speeds; whereas collisions create
pseudo-cohesive forces that make the atmosphere spin faster than its natural
orbital speed for any given distance.

7. Excess spin forces a body to become oblate. More spin
makes it prolate.

Although the nebula was flattened by a shock wave, it is not
perfectly flat and still has some thickness much larger than the dimensions of
a star. So our small, accreting, central proto-star initially takes on a
spherical shape when gravity dominates. As this becomes a coherent liquid body
(even with differential rotation at different depths and different latitudes),
it is forced to spin up by further contraction and accretion, just as a
twirling ice skater will spin up if she pulls in her arms. After more
contraction and spin-up, the equator is forced to bulge outward by centrifugal
forces, while the polar regions tend to drop closer to the center to fill the
void left by the expanded equator material. In short, the shape of the
proto-star changes from spherical to oblate (mildly flattened). The same
phenomenon, increasing oblateness, is happening to the extended atmosphere,
noting only that its outer regions were never very spherical to begin with.
With still more contraction and spin-up, the bulging equator will tend to bulge
out faster on opposite sides along some particular axis, becoming
football-shaped or lemon-shaped. Parts of the equator away from this axis will
tend to flow toward the axis to compensate for density reductions along the
axis when the original material there is stretched along the expanded axis. In
short, the shape becomes prolate, also called a “Maclaurin spheroid”.

8. Overspin causes twin proto-planets to fission from a
proto-star.

If a prolate-shaped body reaches overspin – the state where
centrifugal forces exceed the combination of gravitational and cohesive forces
near the outer ends of the long axis – the end of the larger and more extended
bulging lobe will break off. Its speed is somewhat above orbital speed for its
distance from the proto-star, so it continues its previous motion, but now in a
slightly higher (and slower) orbit around the proto-star instead of attached to
it. Meanwhile, the opposite bulging lobe was itself close to breaking off
because of the symmetry of the prolate shape. When the first lobe breaks off,
the stretched remaining portions of the proto-star just below the broken lobe
are pulled sharply back into the proto-star by gravity. That downward vertical
momentum sends a pressure wave all the way through the proto-star sufficient to
break off most of the opposite lobe. But because the opposite lobe had started
to relax when the proto-star suddenly became smaller, not as much of the
proto-star breaks off as it did for the larger lobe. Empirically, in our solar
system, the opposite lobe has close to 86% of the mass of the larger lobe. (Van
Flandern 2007a: Appendix I) And the second lobe to break off will also have a
closer (and faster) orbit around the changed, smaller proto-star than the first
lobe. In other respects, the two fissioned lobes are destined to become twin
proto-planets, with the outer one always being the more massive of the pair.
And the proto-star left behind has shed mass and momentum, and is no longer in
an overspin state for its new, smaller radius.

Details for how proto-planets evolve into solar system
planets and how that differs from the evolution of moons will be discussed
below. For now, we note here that a solar-type star is dominantly hydrogen, so
all fissioned proto-planets start their existence as dominantly hydrogen bodies
as well. If they are massive enough for their gravity to retain hydrogen, the
lightest and potentially fastest element, the proto-planet will become a
hydrogen-dominated gas giant planet. If a proto-planet is not massive enough to
retain hydrogen, but is massive enough to retain helium, the hydrogen escapes
and the result is a helium-class gaseous planet. It the proto-planet is less
massive than that and most helium escapes too, the planet will likely become a
terrestrial-class solid planet containing mainly elements heavier than helium,
which astronomers like to refer to collectively as “metals”.

See Bejko (2001) for a brief animation of a simple fission.

How solar system planets fit into the fission model

The solar system presently consists of eight major planets
and three dwarf planets. But the distinctions between major planets, dwarf
planets, and moons, or between asteroids and comets, are somewhat arbitrary and
based on broad, general criteria. Marginal cases exist that can be argued
either way. Pluto for example only recently lost its “major planet” status. And
it has been argued that Pluto and its large moon Charon are escaped moons of
Neptune. (Harrington and Van Flandern 1979; Van Flandern 1991)

In the
inner solar system, Van Flandern and Harrington (1976) argued that much of what
we know about Mercury and Venus tells us that Mercury is an escaped Moon of
Venus. More recently, Van Flandern (1997a) suggested that Mars is a former moon
of Bellona (formerly called “Planet V”), the now-exploded planet originally in
an orbit at the distance of Mars from the Sun. The Mercury Messenger spacecraft will evaluate predictions made by the former
hypothesis (see Van Flandern 2007c), while new evidence has already been
supportive of the latter hypothesis. (Van Flandern 2007a and 2007b) These
identity reassignments, as we will see, fit perfectly with the fission model
for solar system origin even though they were deduced from entirely unrelated
considerations long before the modern fission model had been formulated by
anyone. For example, the idea of major planets occurring in twin pairs is
completely missing from the first (1993) edition of my book about the solar
system, although it appears prominently in the second (1999) edition, after I
came to realize the implications of the fission hypothesis. (Van Flandern 1999)

If we
accept these planet/moon identifications for the moment, it is interesting to
look at what is left by way of true, major planets in the original solar
system. First we have Venus and Earth, both rather similar in mass,
composition, solar distance, and number of original significant moons (if our
premise about Mercury is correct). If the exploded planet hypothesis is
accepted, then Bellona (now-exploded parent planet of Mars in a similar orbit
to Mars and associated with S-type asteroids in the inner asteroid belt) and
Planet K (now-exploded planet associated with C-type asteroids in the outer –
and more massive – asteroid belt) would have been another pair, similar in that
they both met the conditions leading to explosion. Following the asteroidal
gap, we have the two largest gas giants, Jupiter and Saturn, likewise with
similar composition and numerous moons, and with masses and solar distances
more similar to one another than to any other existing planet. (We will deal
with the mass difference later.)

Next out we have another pair of twins, Uranus and Neptune,
with similar masses, compositions, and solar distances. Their number of
original significant moons would likewise have been similar if the conjecture
about the origin of Pluto and perhaps also Charon as former Neptunian moons is
correct. Next we have another asteroid belt, called the “trans-Neptunian
objects” (TNOs), beyond the orbit of Neptune near where another planet might
have been expected. And intriguingly, we now have evidence that the TNOs might
come in an inner and an outer belt too, just as the main belt asteroids do.
Three TNOs have been discovered much farther out, with orbits that could not have
shared an origin with the inner TNOs. Could these two sets of asteroids be the
remnants of yet another original pair of twin planets?

One aspect
of this picture is striking: a tendency for these planets to occur in pairs.
Two of these pairs are similar enough for the respective planets to
occasionally be called “twins”: Venus-Earth and Uranus-Neptune. And each pair
is notably and strikingly dissimilar to its adjoining pair or pairs. Now there
is no particular reason under the PSNH of planetary formation why this should
be so. The nebula from which the planets allegedly condensed should have been
rather homogeneous in most respects and planet masses should have had a smooth
radial gradient with solar distance. By contrast, the fission model not only
expects this feature, it demands it, at least for hydrogen-dominated single
stars such as our Sun. Similar remarks with respect to both models apply to the
distribution of angular momentum in the solar system: the PSNH is surprised,
whereas the fission model requires outward migration of angular momentum
through fissioning (the cograv effect).

The fission
hypothesis would also solve the mystery of the dominance of prograde rotation
for these original planets, since they would have shared in the proto-Sun’s
prograde rotation at the outset. By contrast, Lissauer (1992) summarizes this
puzzle from a PSNH perspective: “Almost all the previous calculations were
wrong … If you accrete planets from a uniform disk of planetesimals, the
observed prograde rotation just can’t be explained.” Planets that accreted from
collisions should have random rotations and pole orientations depending on the
random directions of the most significant accreting impacts.

There are
some basic similarities between the solar fission hypothesis for origin of the
planets, and the more traditional accretion from the primeval solar nebula. In
both cases, an extended gas and dust cloud contracts, and a concentration
toward the center eventually becomes dense and hot enough to be classified as a
star. Once that happens, the extended cloud of gas and dust, stabilized in
size, forms a rapidly rotating disk well-outside the inner parts of the
proto-Sun where nuclear fusion may be starting to take place. The core
collapses gravitationally from the inside out, with internal heat stabilizing
the configuration. The disk will tend to continually spin up the central star.
But the fission model notes that the central proto-star cannot continue to
accrete matter from the rapidly rotating disk without occasionally flinging a
significant fraction of it back out. In PSNH, the mechanism for outward mass
transfer is still debated, with some astronomers favoring polar outflow models
and others favoring outflows that originate in the nebular disk (Shu 1992).

However, it
would be incorrect to think of the disk as comprised of numerous discrete
globules that can collide and accrete, as the PSNH requires. Recall that two
bodies in similar orbits around a central mass will go into a state of
libration and avoid collisions. (Van Flandern 1999: chapter 6) The Trojan
asteroids in Jupiter’s orbit, for example, always avoid collision with Jupiter
by librating. All planetary rings are additional examples. Ring particles are
not normally colliding with one another unless the ring is disturbed. Around a
relatively massive primary, the more similar any two orbits are, the more
nearly impossible collision between the bodies in those orbits becomes. So the
accretion feature of PSNH has very little dynamical basis because the
collisions that are allowed (orbits dissimilar by more than the size of the
gravitational sphere of influence of the larger orbiter) are normally
destructive rather than accretive. This problem alone makes PSNH a dubious
proposition.

In fission theory, the initial spin of the proto-planets
would be that of the surface of the proto-Sun, and therefore always prograde.
Subsequent tidal evolution will evolve each twin proto-planet outward (because
the tidal bulge on the proto-Sun leads the proto-planet), with the more massive
of the two evolving outward faster (because it raises the larger bulge).
Although such tidal forces are negligible in the solar system today, they would
have been substantial during the proto-Sun stage, also called its “T Tauri”
phase. Soon after fissioning, the proto-planets would have been within a few
solar radii, assuring very large tidal forces. (Note: At any given distance, each
doubling of the solar radius, or halving of the solar distance, increases such
tidal forces by roughly two orders of magnitude.) Moreover, the proto-planets
would have much larger masses before shedding much of their hydrogen than they
have today, so mutual tides between twin proto-planets would also be large and
significant for subsequent orbital evolution.

Tidal evolution of the mean distance of the proto-planets caused
by the Sun and by each other would typically proceed toward a stable
configuration, wherein each planet has a circular, co-planar orbit with some
simple relation to the orbital period of the next planet in. Once a stable
configuration was achieved, further orbital evolution would cease. Examination
of configurations stable to tidal evolution is a non-trivial subject, touched
on briefly later. One simple example would be the outer planet having double
the orbital period of the inner one (period ratio of 2-to-1). Another common
period ratio would be 5-to-3 because of the interaction of spin periods with
mutual tides and orbital periods with solar-induced tides. A few other stable
configurations exist too.

Special case: The LHB planets

Our picture of the solar system is just what the fission
hypothesis requires, with one glaring exception: Jupiter and Saturn do not
conform to the expectation of a twin pair with an 86% mass ratio and Saturn
having the larger mass of the two. In a previous exposition (Van Flandern
1997b), we conjectured hypothetical Planets A and B in two different
configurations that might account for this, assuming that Jupiter’s mass was
greatly enhanced by absorbing much of the debris when those two planets
exploded. Indeed, we may be confident of the former existence of additional,
large, early members of the planetary system because of the “late heavy
bombardment” (LHB) event. Here is a brief synopsis of that evidence.

From studies of lunar rocks it is now known that the Moon,
and presumably the entire solar system with it, underwent a “late heavy
bombardment” of unknown origin not long after the major planets formed. The
following relevant descriptions of the event are from Weissman (1989):

·“[The
LHB] occurs relatively late in the accretionary history of the terrestrial
planets, at a time when the vast majority of that zone’s planetesimals are
already expected to have either impacted on the proto-planets, or been
dynamically ejected from the inner planets region.”

·“It
appears that a flux of impactors flooded the terrestrial planets region at this
point in the solar system’s history, and is preserved in the cratering record
of the heavily cratered terrain on each planet.”

·“An
essential requirement of any explanation for the late heavy bombardment is that
the impactors be ‘stored’ somewhere in the solar system until they are suddenly
unleashed about 4.0 Gyr ago.”

·“A
plausible explanation for the late heavy bombardment remains something of a mystery.”

·“...
it seems likely that the late heavy bombardment is not the tail-off of
planetary accretion but rather is a late pulse superimposed on the tail-off.
Nor is there any reason to suppose that it was the only such pulse; it may have
been preceded by several others which are not easily discernible from it in the
cratering record.”

So the LHB was a real solar system event. And it would be
most readily explained as the explosion of one or more massive planets in early
solar system history, presumably very massive, hydrogen-dominated planets like
Jupiter and Saturn. That would mean we are missing a pair of planets in the
middle of the solar system. But were they a twin pair? Helium-class twin
planets have shown a tendency to explode (see later discussion), but they are
too limited in mass. The other explosion mechanism apparently operating is
triggered by tidal stress. (Van Flandern 2007a) Massive planets in twin pairs
would be susceptible to extreme tidal stresses. But once the larger twin had
induced the smaller to explode, there would be no mechanism to explode the
survivor. Therefore, we conclude it is most likely that Jupiter and Saturn are
the surviving halves of former twin pairs, and are therefore not themselves an
original twin pair.

It follows that both Jupiter and its presumed twin companion
(“Planet LHB-A”) would have been subject to enormous tidal stresses over a
prolonged period because they were so massive, having retained a major fraction
of their hydrogen; and because they would have made many close approaches
before tidal forces could separate them. Eventually, the combined tidal forces
of the Sun and Jupiter triggered an explosion in LHB-A. Although Saturn is
three times less massive than Jupiter, it is still five times more massive than
Neptune, the next largest surviving planet. So under this scenario, Saturn
would have been the outer and more massive member of another twin pair with a
companion (“Planet LHB-B”). Saturn, like Jupiter, then became a single planet
by eliminating its twin. This would have been the earlier and less massive of
the inferred two LHB explosion events.

It is true
that this scenario may appear to be circular reasoning to the skeptical mind.
Jupiter and Saturn do not fit the fission theory’s requirements; so instead of
falsifying the theory, we propose that each must have disposed of a companion,
thereby conveniently making the hypothesis correct. However, the LHB exists and
was not invented to save this theory, and is consistent with the existence of
one or two more early planets that exploded. Furthermore, the fission theory
clearly does require strong tidal interactions between twin planets soon after
fissioning, which implies there must exist some fissioned mass limit above
which the tidal interactions would be fatally disruptive. Neither of these is
an “add-on helper hypothesis”, motivated just to save the theory. Both are
requirements of the original hypothesis.

Moreover, this particular solution to the Jupiter-Saturn
“exception” has the bonus feature that it explains why many “hot Jupiter”
exoplanets found recently around other stars are single planets and not twins.
Apparently, only the smaller gas giant planet pairs (such as Uranus &
Neptune) can survive the tidal strain of numerous close approaches to another
gas giant soon after fission.

With the Jupiter/Saturn case resolved in this way, and
considering other arguments made some time ago about which planets are escaped
moons and which asteroid belts represent exploded planets, we can now see the
original solar system as composed of six twin-pair proto-planets, with the
inner member of each pair being originally 86% of the mass of the outer in each
pair. See Table I. If Byl and Ovenden (1975) are correct that Jupiter’s mass
has apparently increased by roughly 40% since its asteroidal moons were
captured, then those asteroidal moons predated the main asteroid belt. This
would also imply that the masses shown in the Table for LHB-A and Jupiter, and
probably also LHB-B and Saturn, should all be factored by the factor 5/7 to get
their original masses.

After each
planet pair is formed by fission, it will be some time before the proto-Sun and
its extended atmosphere reach another overspin as they continue to contract. By
that time the Sun will be hotter, more massive, and smaller from accretion and
contraction. So the next pair of planets will fission under rather different
conditions, forming another pair of planets similar to each other but dissimilar
from all previous pairs.

Each gaseous twin proto-planet initially orbits close to the
surface of the parent star. Tidal interactions initially drive the pair
outward, with the more massive outer member of the pair driven faster because
of its greater mass, which causes it to raise larger tides. The direction is
outward because the parent star, while reduced in radius and no longer
over-spinning for its reduced size, nonetheless spins faster than the orbital
speed of either proto-planet; so the tidal bulges raised on the star by each
proto-planet are tidally dragged ahead by the parent star’s rotation, which
then acts to accelerate the proto-planet that raised it. Differential rotation
inside the star has the same effect because rotation gets faster with depth. So
even though the star is gaseous, which tends to diminish longitudinal tides,
radial tides in the star are still quite active on the proto-planets. (Van
Flandern 1999: chapter 12) And the magnitude of these tidal forces is quite
large because they are a strong function of the ratio of star-radius to
planet-distance, a ratio initially near unity. As time goes on, the strength of
tidal forces drops off rapidly because it depends roughly on the seventh power
of the radius-to-distance ratio, which is shrinking both because the proto-planet is
evolving outward and because the star is continuing to contract.

Once the proto-planets are away from the star’s surface and
separated from one another, the star’s tidal forces would eventually drive the
inner planet outward faster than the outer one because the forces are a
stronger function of distance than of mass, and the inner planet is closer to
the star. However, the initial orbits of the two proto-planets produce close
approaches to each other whenever the inner planet passes the outer one. Mutual
tides raised during these encounters raise tidal bulges dragged in the
direction of rotation on each planet. Because that rotation is prograde
(imparted by the star’s own rotation), the bulge on the inner planet raised by
the outer one operates to accelerate the outer planet and move its orbit
outward. At the same time, the tidal bulge on the outer planet raised by the
inner one decelerates the inner planer, opposing the Sun’s tendency to
accelerate it and slowing its outward movement, perhaps even moving it slowly
inward. See Figure 1. So these mutual tidal forces operate to ensure that the
orbits of the two planets continue to separate.

Commonly, direct gravitational perturbations of
proto-planets on each other can increase orbital eccentricities and
instability. However, certain orbital period ratios cause perturbations to
average zero, enhancing stability. The unstable period ratios that increase
eccentricity can result in close approaches again, and a return to large mutual
tidal forces that drive the orbits apart. By contrast, stable orbital period
ratios keep perturbations to a minimum, and therefore are long-lasting
dynamical configurations.

For example, the simplest stable configuration occurs when
one orbital period is exactly double the other, a “resonance” with a 2-to-1
period ratio. This occurs when the distance ratio is ~0.63 or ~1.59. Another
stable configuration (apparently shared by Venus and Earth before Venus shed
its moon Mercury, an event that slightly disrupted the configuration) is a
5-to-3 period ratio. This is because Venus would make exactly 2.5 revolutions
in the time Earth took to make 1.5 revolutions, so close approaches would occur
on alternate sides of the orbits but always at the same spots along both
orbits, causing the mutual perturbations to average to zero. As mutual tidal
forces drive planet orbits away from one another, the strength of the tides
would diminish. However, the frequency of conjunctions (one planet passing by
the other at any distance) would increase because of a greater difference in
orbital periods. So tidal evolution would continue until a combination of
sufficiently weakened tidal forces and a stable (resonant) dynamical
configuration occurred.

These processes can account for the origin of a dozen major
planets. Later, we will examine how it can account for major moons as well.
Fission theory does not need to explain asteroids and comets, which arise
mostly from exploded moons or exploded terrestrial planets. (Van Flandern
2007b) Ordinarily, the explosion of a gaseous planet would leave no solid
debris. But it would tend to impact, add mass to, and destabilize any moons in
its vicinity, possibly causing them to explode at a later date.

Looking beyond Neptune, we note what may be another asteroid
belt, possibly the remnants of an exploded planet in the outer solar system, in
the form of tens of thousands of large fragments in Pluto-like orbits. This is
often referred to as the “Kuiper Belt”, although it apparently has little or
nothing to do with the comets that either Kuiper or more recent astronomers
predicted (Van Flandern 1995). We designate the hypothetical original pre-explosion
planet as “Planet T”, since we prefer to follow the convention of calling the asteroids
in that region TNOs (for Trans-Neptunian Objects).

Recently,
three additional asteroids have been discovered even farther out, with orbits
that cannot reach that of Planet T. This is suggestive of yet another asteroid
belt, much the way the main asteroid belt between Mars and Jupiter has an outer
(“C-type”) portion and an inner (“S-type”) portion, corresponding to the
explosion of twin parent planets K and V, respectively. Future observations
will determine if this is indeed a second outer asteroid belt. Certainly,
fission theory would lead us to expect that Planet T had a twin companion. We
designate it “Planet X” because it would have been the tenth major planet but
for all this revised solar system history. (“X” is the Roman numeral for “ten”,
and “V” is the Roman numeral for “five”.) At one time, hypothetical Planet X
was considered the most likely source of unmodeled perturbations on the gas
giant planets and certain comets. (Van Flandern 1999: chapter 18). But the
failure of searches for it combined with this latest finding of more asteroids
at that rough distance and suggestions that the original masses were in the
“helium-class” range all indicate that Planet X, like helium-class planets V,
K, and T, is now exploded.

In our first publication of the modern fission theory (Van
Flandern 1997b), we noted the existence of the TNOs and commented: “Certainly, [this]
prediction of a *second* planetesimal belt beyond Neptune, if fulfilled, would
be a strong point in favor of the fission theory for the origin of planets.”
Now that a second TNO asteroid belt appears to exist, the prediction takes on
added significance.

So that fills
out the original solar system to distances much beyond which passing stars
would make planet orbits relatively unstable over billions of years. It is
sobering to realize that, if our deductions are valid, fully half of the solar
system’s original planets may have perished in explosions over the past 4.5
billion years. Planets are apparently even more ephemeral than stars, and some
of the events we call “novas” may turn out to be explosions of planets orbiting
the visible star.

Generalizing this scenario’s
methodology, the largest TNOs are probably escaped former moons of Planets T
and X. And something similar can be said about former “Planet K” in the outer
main asteroid belt. The largest asteroid (now a “dwarf planet”) Ceres would
also have been a former moon, and its twin moon probably met the same kind of
fate (explosion) as Body C. So when close-up spacecraft views of Ceres become
available, we expect they will show a hemispheric dichotomy and other
explosion-related similarities to Mars. The lack of atmosphere would probably
mean hard, melting or vaporizing impacts leaving lava-like deposits all over
one hemisphere, but with no obvious source volcanoes for that hemisphere.

Terrestrial and
helium-class planets

For twin planets Earth and Venus, fission
theory indicates that tidal evolution to a 5-to-3 orbital period resonance
occurred between the two. Further simple tidal evolution between Venus and its
fissioned moon Mercury indicates that the escape of Mercury from Venus occurred
about 500 million years later. The present-day circular orbital speed of Venus
is 35.02 km/s, but would have originally needed to be 35.32 km/s to be in the 5-to-3
resonant orbit with Earth (orbital period 7.2 months). However, when Mercury
was still a moon of Venus, its tidal escape would have been through the L1
Lagrange point on the line from Venus to the Sun. As that happens, Mercury’s
relative satellite orbital momentum at escape from Venus is opposite its solar
orbital motion. (This is for the same reason that our Moon’s relative velocity
is opposite to Earth solar orbital velocity at New Moon phase.) This means Mercury’s
escape would have caused a small forward impulse to Venus, giving Venus more
angular momentum but ultimately less orbital speed. Then the strong mutual
tides between Venus and Mercury during the early post-escape period would
separate the orbits further, giving Venus even a bit more angular momentum and
a bit less orbital speed. The inferred drop in Venus’s orbital speed from 35.32
(theoretical) to 35.02 km/s (observed) is an entirely reasonable amount for
these two processes, supporting the starting conjecture that Venus and Earth
were indeed in a resonant 5-to-3 orbital period-lock in the early solar system.

Analogously, as terrestrial proto-planets
were shedding their abundant original (hydrogen and helium) light gases, the
bulk of that mass would likewise preferentially escape through the L1 point. So
the escaping mass leaves terrestrial planets with a net gain in orbital
momentum, and tends to amplify separation of twin planet orbits. This is
another mechanism driving them farther from the Sun and apart from one another.
The same early-mass-loss process for proto-Venus would have accelerated the
tidal escape of Mercury and the rate of recession of our Moon from Earth. The
latter would have allowed proto-Earth, which would become fairly molten again
following the Moon’s fission because of the close Moon’s strong tidal pumping,
to cool and solidify again sooner than simple dynamical models predicted. Our
Moon failed to escape Earth orbit because it is much less massive than Venus’s
former moon Mercury, so the tidal forces our Moon raised were always smaller
than the ones Mercury raised on Venus – one reason why Venus was so much more
volcanically active than Earth long ago.

We note that no corresponding
action pushes a new twin pair into resonance with any pre-existing planet unless
the new pair is fissioned while the old pair is still evolving. So resonances may
never occur between one twin planet pair and the next. However, major moons of
gas giant planets apparently do have 2-to-1 resonances between twin pairs,
suggesting they fission on a much shorter time scale and/or take longer to
evolve. This is consistent with tidal forces between proto-planets and their
moons being stronger than tidal forces between proto-Sun and its planets
because the strength of tidal forces depends more strongly on mutual distance
than on mass.

In overview, fission theory
indicates twelve original major planets, of which six survive. For each twin
pair, the more massive proto-planet (the outermost) would produce intense tidal
stresses on the smaller (innermost) at times of closest approach shortly after
fission from the enlarged proto-Sun. This means these giant twin planets would
never get the chance to evolve into resonance before the smaller was induced to
explode by the larger one. This also explains why many Jupiter-sized exoplanets
(around other stars) apparently have no twin companion.

The fission
hypothesis is a very general mechanism, and explains the formation of all major
moons as well as all major planets. The formation process for major moons is
quite similar to that for planets, with one major exception: The proto-Sun is
accreting mass and gaining spin angular momentum as it does so; whereas
proto-planets are losing mass (they can’t hold all their light gases) and
shedding spin angular momentum. This difference results in the larger of any
fissioned twin pair of moons being the inner one, and causes the operating
tidal forces to move moons inward instead of outward. Both of those circumstances
are opposite to the behavior of fissioned planets.

Another
difference is that proto-stars are all liquid or gaseous, whereas some
proto-planets are solid. When a rotating parent body that is solid or has
substantial material strength, such as proto-Earth or proto-Venus, spins fast
enough to fission, normally just the weaker of the two globules at either end
of the prolate major axis will fission, and the rest of the body will snap back
to a smaller, rounder shape with a slower spin. The spinning parent body gives
away a substantial part of its angular momentum to the fissioned globule. So
only a single moon results, and enough angular momentum is lost that the planet
is unlikely to achieve overspin a second time. Therefore we note that gaseous and
liquid bodies would produce twin pairs by fissioning, whereas solid bodies
would normally produce single moons.

Traditionally, it has been objected that tidal friction
between a fissioned companion body and its gaseous parent ought to be
negligible because the gaseous parent can reshape itself quickly so that any
tidal bulge has no lag or lead, and therefore transfers no angular momentum to
the companion body. If this were the whole story for tides, frictional forces would
be negligible even right after fission, so they could not produce orbit
evolution. However, as explained in Van Flandern (1999: chapter 6), it is not
the usual longitudinal tidal forces described in most textbooks that are
effective for gaseous parent bodies. Those would indeed be negligible for tidal
evolution purposes. Rather, it is latitudinal and radial tidal forces that
matter. For example, a proto-planet causes the proto-Sun to bulge outward, and
a proto-moon does the same to its parent proto-planet.

But the gaseous parent is rotating differentially with
depth. For the proto-Sun, rotation is slower toward its center and faster
toward its surface. So as the proto-Sun bulges outward, part of its slower mass
is raised into layers with faster rotation, thereby causing a leading tidal
bulge. Likewise, gravitational tugs toward the equator of the proto-Sun from a
proto-planet also typically force mass into a latitude band with faster
rotation resulting in a leading bulge. Either process would transfer the excess
angular momentum acquired by the bulge to the proto-planet that raised it,
resulting in outward orbital evolution for the proto-planet. The situation is
just the reverse for the fissioning of proto-moons from a proto-planet because
rotation for a body shedding mass will be faster toward the center and slower
toward the surface. Hence, a tidal bulge is forced to slow as it is pulled to
higher levels or lower latitudes. This results in inward orbital evolution for
the proto-moon that raised the bulge.

Now consider a gaseous proto-planet as the parent body. It
will cool and contract rapidly once away from the proto-Sun, both because it
has no internal heat source and because it is losing mass. Proto-Sun
contraction is much slower because it is accreting mass and heating up. But the
proto-planet would be continuously shedding its light gases as it contracts,
and this mass-shedding carries away spin angular momentum. The gaseous
proto-planet, like the proto-Sun, will acquire differential rotation; but for a
proto-planet shedding mass, the fastest rotation would occur toward its core (where
it is hottest) and the slowest rotation toward its cooler surface. Just like a
proto-star, as the proto-planet contracts, it must spin up to conserve angular
momentum. So the proto-planet can likewise reach an overspin condition. If the
proto-planet is gaseous, a pair of moons will be spawned by the fission
process. But unlike the solar case, the slower differential rotation of the
parent at its surface will cause a tidal bulge lag, which will cause the fissioned
moons to lose angular momentum and spiral slowly inward. The more massive moon
will raise the larger tides and evolve inward the fastest.

Obviously, the proto-planet must continue to contract faster
than its moons evolve inward, or the result would be a cataclysmic merging that
would destabilize the rotation of the proto-planet and tip it over about 90
degrees to minimize its new moments of inertia. Perhaps that is exactly what
happened to Uranus, whose spin axis is tipped over by 98 degrees and whose
remaining natural moons are relatively small for the planet’s size. Having
derived this mechanism deductively from the fission hypothesis, rather than
conjecturing it inductively to explain observations, we might even be justified
to consider it as a mechanism to explain other phenomena too. For example, in
the very last stages of proto-Sun evolution, if the proto-Sun accreted the last
of the solar nebula and briefly expanded rather than contracting, it might have
merged with the “last” fissioned proto-planet pair – a hypothetical pair that
fissioned not far from the present Sun’s surface but never had the chance to
evolve outward. The mass difference of these proto-planets to the proto-Sun
would be too great to cause a tilt as large as 90 degrees. However, their
merger would tilt the proto-Sun somewhat. Today, the Sun has a heretofore
unexplained tilt of 7 degrees to the mean plane of the rest of the planets,
perhaps caused by re-merging with this hypothetical last fissioned planet pair.
A mass merging with a spinning body that is not elongated in a Maclaurin
spheroid shape will produce some degree of rotational instability as the spin
axis seeks to maximize the new moments of inertia.

The remainder of the process is very similar to the proposed
formation of the Moon by fission from an over-spinning Earth (Van Flandern
1999: chapter 14). See Binder (1984) for a diagram and description of this
process as it applies to the fission of the Moon.

Tidal theory predicts that the large, regular moons of the
gas giant planets will occur in twin pairs, with the more massive always being
the inner of the two. How does that prediction compare to reality? The results
are in Table II. Masses are in units of 10-5 of the primary’s mass,
distances are in multiples of the primary’s radius, and periods are in days. We
have included Pluto and Charon as if they are escaped former moons of Neptune,
as suggested by Harrington and Van Flandern (1979). The more recently
discovered dwarf planet Eris and two of the largest TNOs also now make an
appearance. These are all probably former moons. We have compared them to
Neptune for lack of better knowledge about which planet was their actual
parent.

The table points up some interesting patterns among these
major planetary satellites. With Saturn’s large moon Triton excepted, these do
indeed tend to occur in pairs, and the inner member of each pair is always the
more massive, just as the fission theory predicts. This alternating sequence of
satellite masses had not, to this author’s knowledge, been recognized, much
less considered significant, before the fission theory pointed it out.

Jupiter and Uranus have the most regular and apparently
undisturbed large satellite systems: circular and co-planar orbits,
orbit-synchronized spins, with orbital periods roughly double that of the next
moon in. (The small moons are presumed to be captured asteroids.) Correspondingly,
the patterns of these moons contain no exceptions to the requirements of the
fission theory. The closest any of these moon pairs come to an exception would
the larger-than-average mass ratios for the two Jovian pairs, which is larger
than the expected 86% mass ratio rule given by fission theory. However, quoting
from Van Flandern (2007a):

It is almost certainly not a coincidence that the
four major moons of Jupiter are likewise a modest exception to the mass ratio
that applies elsewhere. Indeed, Jupiter is almost certainly accreting mass even
today faster than any other planet. So if its original mass was modified
substantially by the Planet LHB-A & LHB-B explosions, it follows that its
major moons would likewise accrete extra mass. If so, then the innermost of
each moon pair would accrete more because it has faster orbital speed, is more
massive to start with, and lies closer to Jupiter. And this is the direction in
which the observed discrepancies lie for both Jovian pairs, with the
discrepancy being larger for the inner pair as the same idea would predict.

Neptune, of course, has a highly disrupted satellite system.
But the close physical and chemical resemblance between Pluto and Triton has
been noted by many astronomers, making a common origin as moons of Neptune not
at all unlikely. Our task is merely to find the right “twin” for each.
Preliminary mass estimates for Eris (still uncertain by at least several
percent) suggest that Triton is closer to the nominal 86% ratio with Eris than
Pluto is. If so, then Pluto’s mate has yet to be discovered, or met the same
kind of explosion fate as Bellona, the hypothetical twin of Mars. TNOs 2006 EL61 and 2005 FY9 (“Makemake”) are
probably another twin pair of former moons ejected from Planet T when it
exploded. If Planet T was helium class, as we have conjectured, then it
probably was of order 20% of the mass of Neptune. So the relative mass figures
for moons of Planet T should then be multiplied up by a factor of about five.

Neptune’s
moon Nereid, Uranus’s moon Miranda, and all of Saturn’s moons except Titan have
far less than the “one part in 100,000” lower mass limit we adopt here for any
major moon relative to its own parent planet. They are here considered to be
either asteroids or explosion by-products of larger icy moons. Pluto’s
present-day moon Charon may have been another former moon of Planet T, joining
Pluto in an exchange of moons when Planet T had a close encounter with Neptune.
Its partner was most likely ejected into independent solar orbit. This would
parallel the history of Pluto. If so, it awaits discovery as probably the
largest of the still-undiscovered TNOs.

Among the gas giant planets, Saturn is the main surprise.
Its many moons have rather unevenly spaced orbits with several huge gaps,
interspersed with rings of material. It seemed evident that the Saturnian moons
are not in their original orbits even well before this analysis. Now we see yet
another criterion that underscores that disturbed condition: Of Saturn’s eight
original, presumably non-asteroidal moons, only Titan is as large as 10-5
of Saturn’s mass. Titan weighs in at 23.8 x 10-5 of Saturn, making
it the second most massive moon in the solar system, behind only Ganymede. The
next largest Saturnian moon, Rhea, is roughly 50 times smaller in mass. Most of
the others range from a few times 10-6 to a few times 10-8
of Saturn’s mass.

These features imply some sort of disruption event. The
obvious possibility is the explosion of former Planet LHB-B when its orbit was
inside, but still relatively close to, Saturn’s orbit, back near the solar system’s
beginnings. The explosion would have been triggered when the two planets were
close. Large chunks of mass from the exploded gas giant planet could have
impacted hard enough to alter the orbits of then-existing moons, and accreted
enough added mass on other moons to induce them to become unstable and later
explode. The most notable example would have been the twin companion to Titan.
Some of the debris from these secondary explosions would have impacted Saturn
or escaped the planet. But other debris would have survived in the form of
small, icy moons; and tidal forces (still quite strong at those early dates)
would have tended to circularize or regularize their orbits again.

One of the most interesting developments would have been
bringing a major moon close enough to Saturn to allow tidal forces, operating
over billions of years, to gradually bring it inside the Roche “break-up”
limit. The consequence would be the formation of Saturn’s spectacular icy rings
– a unique feature of our solar system. (Other planetary rings are much
smaller, fainter, and composed of finer and darker asteroid-like material.)
Present estimates are that these icy rings of Saturn are less than 100 million
years old because older rings would have been disrupted by micrometeoroid
impacts. But when newer data is analyzed, it may turn out that only the
smallest debris was eliminated. The rings probably now consist of small bodies
with a sharp cut-off on the small-mass side because of the micrometeoroids, and
a sharp cut-off on the large-mass side imposed by the Roche limit tidal forces
for a bodies with the strength of ice. If so, then rings considerably older
than 2% of the age of the solar system are still a possibility for Saturn.

If we make allowance for special cases that have most
probably been altered from their original condition since the solar system’s
beginning, as judged by lines of evidence existing before this analysis began,
we may conclude that the undisturbed solar system members provide a
spectacularly good match to the predictions of the tidal fission theory. That
includes major planets and large, regular moons. And we have used the model to
make several predictions along the way.

But a
scientific theory must be falsifiable as well as make successful predictions.
So we conclude with the obvious prediction that all these same conclusions
about the formation of planets and moons must apply equally well to exoplanets
orbiting other stars, and to their moons. The most easily discovered exoplanets
will be the Jupiter-sized ones, and those will tend to be singles because of
inducing explosion in their companions. And indeed, we already know that lots
of hot Jupiter exoplanets exist-- a big
surprise to the mainstream PSNH theory. But if exoplanets do occur commonly as
twins, that fact would not be immediately evident in the earliest observations
because exoplanets cannot normally be seen, but only inferred to exist from
other data.

With data
of that indirect type, it would be very difficult to recognize that a signal is
caused by two bodies, and the first inference one draws will usually be the
existence of one body on an eccentric orbit. If two bodies have already
established a period resonance with one another, it will be even more difficult
to recognize that two separate planets are involved because it will act even
more like one planet on an eccentric orbit. The wobble of the parent star will
generally make it appear that there is a single orbit of high eccentricity,
when in reality the data reflects the beating of two near-resonance periods. However,
unless the resonance is exact, a longer span of data will reveal the dual
nature of the orbiting planets. We predict that many of the discoveries of
extra-solar planets recently announced will follow that course as the span of
observations lengthens in the coming years, and as more Neptune-to-Earth-sized
exoplanets are discovered.

Even more
to the point, the standard model and fission theory make opposite predictions
about the direction of tidal evolution. The surprising (to the standard model)
number of “hot Jupiters” close to their parent star must be driven inward by
tidal forces in the standard model, but driven outward by tidal forces in the
fission model. This direction of orbital evolution is slow in a human lifetime,
so this measurement is difficult. But perhaps a case will be found where the
spin of the star and the orbit of the planet can be shown to be in the same
direction, with the star spinning faster than the planet’s orbital period. That
would be indirect proof that the direction of tidal evolution was outward.

Appendix A – Why a supernova flattens a nebula

Most interstellar nebulas are made primarily of hydrogen
atoms. The blast wave consists mainly of ions -- protons and electrons --
traveling at high speed. So the numerous impulses to each nebula atom from the
blast wave ions are statistically fairly similar.

Suppose we have two atoms, A and B, at rest with respect to
each other and at different distances from the supernova. Let the blast wave
encounter A first, and accelerate A to nearly the blast wave speed. Sometime
later the blast wave encounters B and accelerates B to the same high speed. So
A & B end up with no relative speed, but nearly at the same distance from
the supernova. Their radial separation will have been "flattened". In
fact, some flattening must occur even if the acceleration were limited to much less
than the blast wave speed because A is accelerated sooner than B.

A second factor is “speed flattening”.
Suppose atoms A and B have no radial motion relative to the supernova, but atom
B has a small speed s relative to atom A in
the direction perpendicular to the supernova. If a blast wave from the
supernova applies a radial speed of S
to both atoms, then the speed of A will be increased from zero to S. However, the final speed of B will become
because these two speeds are at right angles.
If S is large compared to s, then (by expanding the
square root) atom B's final speed is approximately . So
the speed difference between A and B is just ,
which is equal to . This
is obviously much less than the initial speed difference s if S?s. So the cloud atoms end
up with smaller relative speeds than they started with. And this means they
will have a greater tendency to collapse under the influence of gravity.

Appendix B – The meaning of “heat” for small particles

When something small hits something big and gets absorbed
instead of rebounding, usually some of the impactor's kinetic energy gets
absorbed and redistributed into the molecular vibration speeds in the larger
body. We call this adding heat and causing an increase in the temperature of
the larger body, even though we cannot directly measure the change in molecular
vibration speeds. The added heat resulting from an asteroid hitting the Earth
would be obvious. If instead, a globular cluster hits a galaxy, that would
cause an increased average speed of both the galaxy's and the cluster's
interacting stars near the site of impact.

On a quantum scale, the same principles
apply even though we have no way to observe heat activity at that level. When
molecules impact one another, they vibrate faster. When ions impact one another,
the extra "speed" must be deposited in the constituents making up the
ion, or else in the elysium[1]
atmosphere surrounding it. "Heat" must always manifest itself as
increased speed, but we cannot yet hope to directly observe constituents of
ions with existing instrumentation. We can just say with confidence that the
colliding "dust" particles of whatever type in a nebula will get
hotter.

Appendix C – Solid vs. liquid vs. gaseous phases

In the universe, conservation of momentum is fundamental and
absolute because substance and motion can be neither created from nothing nor
vanish into nothing. The conservation of energy is also usually true. But
energy is harder to track because we can’t observe where it goes if large
bodies break off pieces too small and/or too fast to observe. And conversely,
when small, fast entities are absorbed by a larger one, their absorbed motion
often takes the form of heat or vibration and becomes unobservable.

Far out in the collapsing interstellar cloud, we call its
low-density contents a gas. The denser, closer regions tend to be hotter
because of more frequent collisions. This heat is manifested in either translational
speeds or vibration speeds of molecules, or perhaps similar motions on the
quantum level. The same kind of heat gradient occurs in planetary atmospheres,
which retain heat better at lower altitudes.

In a region
where the particle density becomes so great that the individual particles (of
whatever size) have little freedom to move independently, but can only vibrate and
continuously bang into nearby neighbors, the gas can become a liquid. The
transition occurs when there is no more room for translational motion so
molecules have limited ability to migrate, and heat is entirely by vibration.
If the density increases further without corresponding heat increase, or if
heat is lost, the molecules may become locked in place, unable to move except
in a shared motion with their locked neighbors, in which case we have a solid.

Appendix D – The origin of spin

Inhomogeneities (density variations) in the original nebula
and in the supernova blast wave that invades it will create matter
concentrations in the flattened nebula. The same inhomogeneities produce small,
random torques, leaving each matter concentration with some small net spin.
Then the matter concentration gravitationally attracts atoms from the
surrounding nebula, and begins to grow in size. Let’s track what happens to a
single atom falling at random into such a matter concentration destined to
become a proto-star.

The falling atom starts out in the newly flattened nebula as
an independent agent with its own small random motion. If it did not collide
with anything along the way, it would simply pick up speed as it fell, and its
trajectory would be an elliptical orbit around (or through) the matter
concentration. The farther it falls toward the center of the mass
concentration, the more speed it will pick up, slowing again only after it
passes the pericenter of its elliptical orbit.

Now suppose the atom A strikes another identical atom B
already in the matter concentration and participating in its small net spin.
The most probable place for the strike to occur is near the pericenter of A’s
orbit, where the mass concentration is densest and the existing net spin is fastest.
If A catches up to B and strikes it from behind, the relative speed of the two
atoms is minimal, and A’s linear momentum simply adds angular momentum (spin)
to the matter concentration by joining it and by accelerating the forward
motion of B. However, if A strikes B head-on, the relative speed is maximal,
and a larger fraction of A’s linear momentum is converted to heat (vibration).
The two atoms lose orbital speed, but that causes them to drop to a lower
orbit, picking up speed again as they drop. Subsequent encounters assure that
each atom will take on the speed and direction appropriate for its distance
from the center of the matter concentration, which is then the only way it can
avoid continuing collisional encounters.

The net result of a new atom joining a matter concentration
can range from adding all its linear momentum to the angular momentum of the
concentration at one extreme, or to subtracting part of its linear momentum
from the angular momentum of the concentration at the other extreme. So on
average, accretion of new atoms adds angular momentum (spin) to a matter
concentration and heats it up at the same time. Accreting bodies will continue
to spin up until the source for accretion is exhausted, or until the accreting
body reaches overspin and fissions.